A Study of Quasi-parton Distribution Functions in the Diquark Spectator Model

TL;DR

This study evaluates quasi-parton distribution functions within the diquark spectator model to determine their accuracy compared to standard PDFs at various nucleon momenta, providing guidance for lattice QCD calculations.

Contribution

It offers a detailed analysis of quasi-PDFs for all leading-twist distributions in the diquark model, clarifying their validity range and limitations.

Findings

Quasi-PDFs approximate standard PDFs within 20-30% for intermediate x when Pz ≥ 1.5-2 GeV.

Higher Pz > 4 GeV is needed for large x (~1) to match PDFs.

The Soffer bound does not generally hold for quasi-PDFs.

Abstract

To facilitate lattice QCD calculations of nucleon structute, a set of quasi-parton distributions were recently introduced. These quasi-PDFs were shown to reduce to standard PDFs when the nucleon is boosted to high energies, $P_z\rightarrow \infty$. Since taking such limit is not feasible in lattice simulations, it is essential to provide guidance for what values of $P_z$ the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolarized distribution $f_1$, helicity distribution $g_1$, and transversity distribution $h_1$). We find that, for intermediate parton momentum fractions $x$, quasi-PDFs are good approximations to standard PDFs (within $20-30\%$) when $P_z\gtrsim 1.5-2$ GeV. On the other hand, for large $x\sim 1$ much larger $P_z > 4$ GeV is necessary to obtain a satisfactory agreement between the two sets. We further find that the Soffer positivity bound does not hold in general for quasi-PDFs.